Topological Library - Part 3: Spectral Sequences In Topology

by Serguei Petrovich Novikov

Author	: Serguei Petrovich Novikov
Publisher	: World Scientific
Total Pages	: 590
Release	: 2012-07-25
Genre	: Mathematics
ISBN	: 9814401323

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The final volume of the three-volume edition, this book features classical papers on algebraic and differential topology published in the 1950s-1960s. The partition of these papers among the volumes is rather conditional. The original methods and constructions from these works are properly documented for the first time in this book. No existing book covers the beautiful ensemble of methods created in topology starting from approximately 1950. That is, from Serre's celebrated “singular homologies of fiber spaces.”

Topological Library

by Serge? Petrovich Novikov

Author	: Serge? Petrovich Novikov
Publisher	: World Scientific
Total Pages	: 590
Release	: 2012
Genre	: Mathematics
ISBN	: 9814401315

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The final volume of the three-volume edition, this book features classical papers on algebraic and differential topology published in 1950-60s. The original methods and constructions from these works are properly documented for the first time in this book. No existing book covers the beautiful ensemble of methods created in topology starting from approximately 1950. That is, from Serre's celebrated "singular homologies of fiber spaces."

New Ideas In Low Dimensional Topology

by Vassily Olegovich Manturov

Author	: Vassily Olegovich Manturov
Publisher	: World Scientific
Total Pages	: 541
Release	: 2015-01-27
Genre	: Mathematics
ISBN	: 9814630632

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This book consists of a selection of articles devoted to new ideas and developments in low dimensional topology. Low dimensions refer to dimensions three and four for the topology of manifolds and their submanifolds. Thus we have papers related to both manifolds and to knotted submanifolds of dimension one in three (classical knot theory) and two in four (surfaces in four dimensional spaces). Some of the work involves virtual knot theory where the knots are abstractions of classical knots but can be represented by knots embedded in surfaces. This leads both to new interactions with classical topology and to new interactions with essential combinatorics.

Topological Library - Part 2: Characteristic Classes And Smooth Structures On Manifolds

by Serguei Petrovich Novikov

Author	: Serguei Petrovich Novikov
Publisher	: World Scientific
Total Pages	: 278
Release	: 2009-10-07
Genre	: Mathematics
ISBN	: 9814469297

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This is the second of a three-volume set collecting the original and now-classic works in topology written during the 1950s-1960s. The original methods and constructions from these works are properly documented for the first time in this book. No existing book covers the beautiful ensemble of methods created in topology starting from approximately 1950, that is, from Serre's celebrated “singular homologies of fiber spaces.”

Adex Theory: How The Ade Coxeter Graphs Unify Mathematics And Physics

by Saul-paul Sirag

Author	: Saul-paul Sirag
Publisher	: World Scientific
Total Pages	: 277
Release	: 2016-01-25
Genre	: Mathematics
ISBN	: 9814656518

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This book shows how the ADE Coxeter graphs unify at least 20 different types of mathematical structures. These mathematical structures are of great utility in unified field theory, string theory, and other areas of physics.

Mathematics Of Harmony As A New Interdisciplinary Direction And "Golden" Paradigm Of Modern Science - Volume 2: Algorithmic Measurement Theory, Fibonacci And Golden Arithmetic's And Ternary Mirror-symmetrical Arithmetic

by Alexey Stakhov

Author	: Alexey Stakhov
Publisher	: World Scientific
Total Pages	: 331
Release	: 2020-09-03
Genre	: Mathematics
ISBN	: 9811213488

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Volume II is the second part of the 3-volume book Mathematics of Harmony as a New Interdisciplinary Direction and 'Golden' Paradigm of Modern Science. 'Mathematics of Harmony' rises in its origin to the 'harmonic ideas' of Pythagoras, Plato and Euclid, this 3-volume book aims to promote more deep understanding of ancient conception of the 'Universe Harmony,' the main conception of ancient Greek science, and implementation of this conception to modern science and education.This 3-volume book is a result of the authors' research in the field of Fibonacci numbers and the Golden Section and their applications. It provides a broad introduction to the fascinating and beautiful subject of the 'Mathematics of Harmony,' a new interdisciplinary direction of modern science. This direction has many unexpected applications in contemporary mathematics (a new approach to a history of mathematics, the generalized Fibonacci numbers and the generalized golden proportions, the generalized Binet's formulas), theoretical physics (new hyperbolic models of Nature) and computer science (algorithmic measurement theory, number systems with irrational bases, Fibonacci computers, ternary mirror-symmetrical arithmetic).The books are intended for a wide audience including mathematics teachers of high schools, students of colleges and universities and scientists in the field of mathematics, theoretical physics and computer science. The book may be used as an advanced textbook by graduate students and even ambitious undergraduates in mathematics and computer science.

New Horizons For Second-order Cybernetics

by Alexander Riegler

Author	: Alexander Riegler
Publisher	: World Scientific
Total Pages	: 405
Release	: 2017-09-15
Genre	: Computers
ISBN	: 9813226277

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In almost 60 articles this book reviews the current state of second-order cybernetics and investigates which new research methods second-order cybernetics can offer to tackle wicked problems in science and in society. The contributions explore its application to both scientific fields (such as mathematics, psychology and consciousness research) and non-scientific ones (such as design theory and theater science). The book uses a pluralistic, multifaceted approach to discuss these applications: Each main article is accompanied by several commentaries and author responses, which together allow the reader to discover further perspectives than in the original article alone. This procedure shows that second-order cybernetics is already on its way to becoming an idea shared by many researchers in a variety of disciplines.

Quipu: Decorated Permutation Representations Of Finite Groups

by Yongju Bae

Author	: Yongju Bae
Publisher	: World Scientific
Total Pages	: 456
Release	: 2024-06-27
Genre	: Mathematics
ISBN	: 9811292779

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This book studies dihedral groups, dicyclic groups, other finite subgroups of the 3-dimensional sphere, and the 2-fold extensions of the symmetric group on 4 letters from the point of view of decorated string diagrams of permutations. These are our metaphorical quipu. As you might expect, the book is replete with illustrations. In (almost) all cases, explicit diagrams for the elements of the group are given. The exception is the binary icosahedral group in which only the generators and relations are exhibited.

Mereon Matrix, The: Everything Connected Through (K)nothing

by Jytte Brender Mcnair

Author	: Jytte Brender Mcnair
Publisher	: World Scientific
Total Pages	: 903
Release	: 2018-06-08
Genre	: Mathematics
ISBN	: 9813233575

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In this richly illustrated book, the contributors describe the Mereon Matrix, its dynamic geometry and topology. Through the definition of eleven First Principles, it offers a new perspective on dynamic, whole and sustainable systems that may serve as a template information model. This template has been applied to a set of knowledge domains for verification purposes: pre-life-evolution, human molecular genetics and biological evolution, as well as one social application on classroom management.The importance of the book comes in the following ways: